Ruedenberg

Schmidt M W and Ruedenberg K 1979 Effective convergence to compiete orbitai bases and to the atomic Hartree-Fock iimit through systematic sequences of Gaussian primitives J. Chem. Phys. 71 3951-62... 

As shown by Valtazanos and Ruedenberg [93], steepest descent paths (e.g., the Fiikui intrinsic reaction coordinate)... 

Sun J-Q and Ruedenberg K 1993 Quadratic steepest descent on potential energy surfaces. I. Basic formalism and quantitative assessment J. Chem. Phys. 99 5257... 

Valtazanos P and Ruedenberg K 1986 Bifurcations and transition states Theor. Chim. Acta 69 281... 

Even-tempered basis sets (M. W. Schmidt and K. Ruedenberg, J. Chem. Phys. 71, 3961 (1979)) consist of GTOs in which the orbital exponents ak belonging to series of orbitals consist of geometrical progressions ak = a, where a and P characterize the particular set of GTOs. 

The Edmiston-Ruedenberg localization scheme uses the inverse of the distance between two electrons as the operator, and maximizes the expectation value. 

There is little experience with the von Niessen method, but for most molecules the remaining three schemes tend to give very similar LMOs. The main exception is systems containing both a- and vr-bonds, such as ethylene. The Pipek-Mezey procedure preserves the cr/yr-separation, while the Edmiston-Ruedenberg and Boys schemes produce bent banana bonds. Similarly, for planar molecules which contain lone pairs (like water), the Pipek-Mezey method produces one in-plane cr-type lone pair and one out-of-plane yr-type lone pair, while the Edmiston-Ruedenberg and Boys schemes produce two equivalent rabbit ear lone pairs. 

Although the localization by energy criteria (Edmiston-Ruedenberg) may be considered more fundamental than one based on distance (Boys) or atomic charge (Pipek-Mezey), the difference in computational effort means that the Boys or Pipek-Mezey procedures are often used in practice, especially since there is normally little difference in the shape of the final LMOs. 

Ham, N. S., and Ruedenberg, K., J. Chem. Phys. 25, 1, 13, Electron interaction in the free-electron network model for conjugated systems. I. Theory. II. Spectra of aromatic hydrocarbons."... 

Molecular orbital bonding concepts in polyatomic molecules a novel pictorial approach. D. K. Hoffman, K. Ruedenberg and J. G. Verkade, Struct. Bonding (Berlin), 1977, 33, 57-96 (14). 

Hoffmann DK, Ruedenberg K, Verkade JG (1977) Molecuar Orbital Bonding Concepts in Polyatomic Molecules - A Novel Pictorial Approach. 33 57-96 Hogenkamp HPC, Sando GN (1974) The Enzymatic Reduction of Ribonucleotides. 20 23-58 Housecroft CE (1997) Clusters with Interstitial Atoms from the p-Block How Do Wade s Rules Handle Them 87 137-156 Huber R, see Romao MJ (1998) 90 69-96... 

Leo Radom (Canberra, Australia) Klaus Ruedenberg (Ames, Iowa) Henry F. Schaefer III (Athens, Georgia) Isaiah Shavitt (Columbus, Ohio)... 

Sets of orbital exponents r (/, k) have been proposed mainly by Huzinaga [3], van Duijneveldt [4], Pople et al. [5]. A systematic construction of basis sets of arbitrary dimension is possible in terms of the even tempered concept of Ruedenberg et al. [6,7 ], or of some more sophisticated generalizations [8,9,10]. For a recent comprehensive review on basis sets see Feller and Davidson [11]. 

Hoffmann, D. K., Ruedenberg, K., Verkade, J. G. Molecular Orbital Bonding Concepts in Polyatomic Molecules - A Novel Pictorial Approach. Vol. 33, pp. 57-96. 

Atchity GJ, Xantheas SS, Ruedenberg K (1991) Potential energy surfaces near intersections. J Chem... 

Step 2. The set of CMOs orthogonal molecular orbitals (LMOs) Xj using, e.g., Ruedenberg s localization criterion205. This is achieved by multiplying up with an appropriate unitary transformation matrix L ... 

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